The ability to characterize arbitrary and non-repetitive optical waveforms with sub-picosecond (sub-ps) resolution in single-shot and in real-time is beneficial in different fields, such as advanced optical communication [1, 2], ultrashort pulses generation [3, 4], optical devices evaluation [5] and ultrafast bio-imaging [6, 7]. The references identified in square brackets are listed below and are incorporated herein by reference in their entirety.
More importantly, it has helped reveal fascinating ultrafast phenomena in optics, such as the onset of mode-locking [8, 9], soliton explosions [10-11] and optical rogue waves [12-14. Temporal imaging system is one of the most promising techniques perceived and developed to meet the needs of single-shot, real-time waveform characterization [15-17]. Based on space-time duality [15-17], quadratic phase modulation (time-lens) and dispersion can be properly combined to significantly increase the time-domain detection bandwidth. On the other hand, just like there are always limitations on the field-of-view in any spatial imaging system, the single-shot record length ΔT or the temporal aperture of temporal imaging systems has previously been limited to less than 300 ps [18].
Owing to this limitation, the time-bandwidth product (“TBWP”), ratio between the maximum record length ΔT and temporal resolution δt of state-of-the-art temporal imaging systems [19] has not exceeded 450. Such a situation hinders the applications of temporal imaging systems to the study of many important optical nonlinear dynamic phenomena, where not only fine temporal details but also long evolution information are necessary for a comprehensive understanding of the phenomena. For example, studying the dynamics of dissipative Kerr solitons in microresonators [20] is of particular interest because of its potential applications in low-phase noise photonic oscillators [21], broadband optical frequency synthesizers [22], and coherent terabit communications [23]. While the soliton generation benefits greatly from the ultrahigh quality factor (Q) of the microresonator, the ultrahigh Q also renders its formation and transition dynamics slowly evolved at a time scale much longer than the cavity roundtrip time [24, 25], which causes significant challenges in the experimental real-time observation.
Similarly, an optical metrology system that combines the feats of fine temporal resolution and long measurement window is also desired in the study of optical turbulence and laminar-turbulent transition in fiber lasers [26, 27], which leads to a better understanding of coherence breakdown in lasers and laser operation in far-from-equilibrium regimes. To capture comprehensive portraits of these processes, a temporal imaging system with a TBWP much greater than 1,000 is necessary.
Meanwhile, limitations on TBWP also exist for other techniques that achieve comparable performance [28-32]. Single-shot real-time spectral interferometry [32] has been adopted to reconstruct the time-domain information, achieving a temporal resolution (δt) of 400 fs. However, its temporal record length is limited by the spectral resolution (10 pm) to around 350 ps, which results in a TBWP of 875.
Another measurement technique combines spectral slicing of the optical signal with parallel optical homodyne detection using a frequency comb as a reference [31]. Even though a TBWP larger than 320,000 has been demonstrated at a 160-GHz detection bandwidth, it is practically challenging to scale the detection bandwidth beyond 1 THz (i.e., sub-ps temporal resolution). Acknowledging current existing methods, a waveform measurement technique achieving sub-ps temporal resolution and a scalable record length simultaneously is urgently needed and it would be a powerful tool for studying ultrafast dynamics in different areas.